Characterising memory in infinite games

This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-or...

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Veröffentlicht in:Logical methods in computer science Jg. 21, Issue 1
Hauptverfasser: Casares, Antonio, Ohlmann, Pierre
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Logical Methods in Computer Science Association 24.03.2025
Logical Methods in Computer Science e.V
Schlagworte:
Computer Science
computer science - formal languages and automata theory
computer science - logic in computer science
Universal graphs
Infinite duration games
Memory
ISSN:1860-5974, 1860-5974
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Zusammenfassung:This paper is concerned with games of infinite duration played over potentially infinite graphs. Recently, Ohlmann (LICS 2022) presented a characterisation of objectives admitting optimal positional strategies, by means of universal graphs: an objective is positional if and only if it admits well-ordered monotone universal graphs. We extend Ohlmann's characterisation to encompass (finite or infinite) memory upper bounds. We prove that objectives admitting optimal strategies with $\varepsilon$-memory less than $m$ (a memory that cannot be updated when reading an $\varepsilon$-edge) are exactly those which admit well-founded monotone universal graphs whose antichains have size bounded by $m$. We also give a characterisation of chromatic memory by means of appropriate universal structures. Our results apply to finite as well as infinite memory bounds (for instance, to objectives with finite but unbounded memory, or with countable memory strategies). We illustrate the applicability of our framework by carrying out a few case studies, we provide examples witnessing limitations of our approach, and we discuss general closure properties which follow from our results.
ISSN:1860-5974
1860-5974
DOI:10.46298/lmcs-21(1:28)2025